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- W1993159688 abstract "Given a Lie superalgebra g, we introduce several variants of the representation ring, built as subrings and quotients of the ring R_{Z_2}(g) of virtual g-supermodules (up to even isomorphisms). In particular, we consider the ideal R_{+}(g) of virtual g-supermodules isomorphic to their own parity reversals, as well as an equivariant K-theoretic super representation ring SR(g) on which the parity reversal operator takes the class of a virtual g-supermodule to its negative. We also construct representation groups built from ungraded g-modules, as well as degree-shifted representation groups using Clifford modules. The full super representation ring SR^{*}(g), including all degree shifts, is then a Z_{2}-graded ring in the complex case and a Z_{8}-graded ring in the real case. Our primary result is a six-term periodic exact sequence relating the rings R^{*}_{Z_2}(g), R^{*}_{+}(g), and SR^{*}(g). We first establish a version of it working over an arbitrary (not necessarily algebraically closed) field of characteristic 0. In the complex case, this six-term periodic long exact sequence splits into two three-term sequences, which gives us additional insight into the structure of the complex super representation ring SR^{*}(g). In the real case, we obtain the expected 24-term version, as well as a surprising six-term version of this periodic exact sequence." @default.
- W1993159688 created "2016-06-24" @default.
- W1993159688 creator A5022632048 @default.
- W1993159688 date "2004-03-12" @default.
- W1993159688 modified "2023-09-27" @default.
- W1993159688 title "Representation rings of Lie superalgebras" @default.
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